Research with High School Students

As an high school outreach program, I invite brilliant and talented young minds in nearby high schools for a research experience in mathematical sciences.

  • Current Research Projects

    • None

  • Past Research Projects

    • Timelike Surfaces of Revolution with Constant Mean Curvature in de Sitter 3-Space

      • Status: Complete, Summer 2013 - Fall 2013
      • Student: Jacob Martin, Oak Grove High School (Senior)
      • Project Synopsis: In this project, we construct timelike surfaces of revolution with constant mean curvature \(H=c\) and minimal timelike surfaces of revolution in de Sitter 3-space \(\mathbb{S}^3_1(c^2)\) of constant sectional curvature \(c^2\). We show that timelike surfaces of revolution with constant mean curvature \(H=c\) in \(\mathbb{S}^3_1(c^2)\) tend toward a timelike catenoid, the minimal timelike surface of revolution in Minkowski 3-space \(\mathbb{R}^{2+1}\) as \(c\to 0\). Minimal timelike surfaces of revolution in \(\mathbb{S}^3_1(c^2)\) also tend toward the timelike catenoid in \(\mathbb{R}^{2+1}\) as \(c\to 0\).
      • Publication:

        International Electronic Journla of Geometry, Volume 8 (2015), No. 1, 116-127. Preprint is available here.

      • Animations: We made some animations in regard to this project.

        • Animation 1: Animation of CMC \(H=c\) timelike surfaces of revolution in \(\mathbb S^3_1(c^2)\) tending toward timelike catenoid in \(\mathbb R^{2+1}\) as \(c\to 0\).
        • Animation 2: Animation of minimal timelike surfaces of revolution in \(\mathbb S^3_1(c^2)\) tending toward timelike catenoid in \(\mathbb R^{2+1}\) as \(c\to 0\).